An XFEM method for modeling geometrically elaborate crack propagation in brittle materials

Abstract

SUMMARYWe present a method for simulating quasistatic crack propagation in 2-D which combines the extended finite element method (XFEM) with a general algorithm for cutting triangulated domains, and introduce a simple yet general and flexible quadrature rule based on the same geometric algorithm. The combination of these methods gives several advantages. First, the cutting algorithm provides a flexible and systematic way of determining material connectivity, which is required by the XFEM enrichment functions. Also, our integration scheme is straightforward to implement and accurate, without requiring a triangulation that incorporates the new crack edges or the addition of new degrees of freedom to the system. The use of this cutting algorithm and integration rule allows for geometrically complicated domains and complex crack patterns.

Adaptation of engineering FEA-based algorithms to LCF failure and material data prediction in offshore design

“…These are the works on time-evolving phenomena of crack propagation (Biglari et al, 2006) and yield zone stability (Kang, 2008). Evolution of the crack and plastic zone is a coupled material-structural phenomenon, and often requires extensions of standard FEA, like XFEM (Richardson et al, 2011) or efficient shakedown predicting methods (Spiliopoulos and Panagiotou, 2012). This paper faces both the material-related and geometrical issues.…”

A fully automatic polygon scaled boundary finite element method for modelling crack propagation

“…The extended FEM (XFEM) [12] and meshless methods [13] using nodal enrichment techniques, which can model crack propagation without remeshing, have been proposed more recently as alternatives to tackle the difficulties faced by the FEM in crack propagation modelling. Serious crack propagation problems both in statics and dynamics have been solved with these two methods [14][15][16][17]. However, fine meshes (in the case of XFEM) and fine nodal distributions (in the case of meshless methods), are still needed, especially when the crack paths are unknown in advance [18].…”

Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM

“…Namely among them are Belytschko et al (2003), Sukumar and Prevost (2003), Bellec and Dolbow (2003), Sukumar et al (2005), Belytschko et al (2005), Asadpoure et al (2006a, b), Sladek et al (2006), Asadpoure and Mohammadi (2007), Belytschko and Gracie (2007), Tabarraei and Sukumar (2008), Giner et al (2009), Abdelaziz and Hamouine (2008), Ebrahimi et al (2008), Shibanuma and Utsunomiya (2009), Richardson et al (2009), Liang et al (2010), Hattori et al (2012), Mousavi and Sukumar (2010), Ghorashi et al (2011) and Chatzi et al (2011).…”